Shear Strength Applications in Plastic and Limit Equilibrium - Unsaturated Soil Mechanics in Engineering Practice - page 647

Y

Entry point

Search grid or
output grid

j

R i

Initial
point

S i

k

Search
boundary

i i + 1

A

Exit point

Grid element

Y B

Final point

State point

B

X

1 i i + 1 X B i n + 1 Stage no.

Figure 12.82 Scheme for use of dynamic programming method in slope stability analysis.

that the entire trial segment in which the actuating force
is being calculated should be eliminated from the search.
Applying this condition to the optimization procedure
eliminates all trial segments that constitute kinky shaped
slip surfaces.

12.6.1.5 Restrictions on Shape of Critical Slip Surface
The shape of the critical slip surface must be kinematically
admissible. Baker (1980) assumed that the critical slip sur-
face must be concave. Baker (1980) proposed that the first
derivative calculated from the crest to the toe of the slope
must be greater than or at least equal to zero. Zou et al.,
(1995) stated that a check must be made to assure that
the critical slip surface is kinematically admissible. Kine-
matical restrictions play an important role in applying the
dynamic programming method in slope stability analysis.
Using appropriate kinematical restrictions prevents the shape
of the critical slip surface from being unreasonable.
Failure takes place when the resisting force and the actu-
ating force along the slip surface are in contrary directions.
The resisting force must act in the direction opposite to
the mass movement. The actuating force must also be in
the same direction as mass movement (Fig. 12.83). If the
actuating force calculated is in a contrary direction to the
anticipated direction of mass movement, then it is suggested

12.6.2 Example Solutions Using Dynamic
Programming
The results from a number of example problems are pre-
sented. The results are compared to factors of safety obtained
using other methods of slope stability analysis.

12.6.2.1 Simple Homogeneous Slope
The stability of a simple homogeneous slope at 2:1 is exam-
ined. The soil stress states and pore-water pressures are
computed using a partial differential solver with a linear
elastic constitutive model. The slope has a groundwater table
that passes 4m below the crest of the slope and proceeds to
the toe of the slope, as shown in Fig. 12.84.

Eliminated

Y Kinematical restriction

R 1 > < S 1

R 2 > < S 2

j

...

S i

R i > < S i

A

R i

...

k

i

S 1 i + 1

R 1

R n > < S n

S 2

R 2

S 3

S 6

B

S 4

S 5

R 3

R 4

R 6

R 5

X

Figure 12.83 Kinematical restrictions applied to shape of critical slip surface.